Boil the potatoes with the skin on until cooked, then peel them.
Place the potatoes in a bowl and mash them well.
Thinly slice cucumber, onion, and carrot, then salt them to pickle.
Squeeze out the excess water from the pickled vegetables.
Finely chop the hard-boiled egg.
Add potatoes, vegetables, eggs, mayonnaise, and salt, and mix well.
Taste and season with pepper to your preference.